Tunable optical filter

ABSTRACT

The present invention relates to a tunable optical filter having a variable wavelength characteristic of transmittance. The tunable optical filter includes first and second polarizers each having a transmission axis determining a polarization axis of transmitted polarized light, a birefringent element having an optic axis determining a phase difference given between two orthogonal components of transmitted polarized light, and a Faraday rotator for giving a variable Faraday rotation angle to transmitted polarized light. The birefringent element and the Faraday rotator are provided between the first and second polarizers. The order of arrangement of the birefringent element and the Faraday rotator, and the relative positional relation between the optic axis of the birefringent element and the transmission axis of each polarizer are set so that the shape of a characteristic curve giving a wavelength characteristic of transmittance changes along a transmittance axis according to a change in the Faraday rotation angle.

BACKGROUND OF THE INVENTION

[0001] 1. Field of the Invention

[0002] The present invention relates generally to a tunable opticalfilter applicable to a system such as an optical fiber communicationsystem, and more particularly to a tunable optical filter in which theshape of a characteristic curve giving a wavelength characteristic oftransmittance changes along a transmittance axis.

[0003] 2. Description of the Related Art

[0004] In recent years, a manufacturing technique and using techniquefor a low-loss (e.g., 0.2 dB/km) optical fiber have been established,and an optical fiber communication system using the optical fiber as atransmission line has been put to practical use. Further, to compensatefor losses in the optical fiber and thereby allow long-haultransmission, the use of an optical amplifier for amplifying signallight has been proposed or put to practical use.

[0005] An optical amplifier known in the art includes an opticalamplifying medium to which signal light to be amplified is supplied andmeans for pumping the optical amplifying medium so that the opticalamplifying medium provides a gain band including the wavelength of thesignal light. For example, an erbium doped fiber amplifier (EDFA)includes an erbium doped fiber (EDF) as the optical amplifying mediumand a pumping light source for supplying pump light having apredetermined wavelength to the EDF. By preliminarily setting thewavelength of the pump light within a 0.98 μm band or a 1.48 μm band, again band including a wavelength of 1.55 μm can be obtained. Further,another type optical amplifier having a semiconductor chip as theoptical amplifying medium is also known. In this case, the pumping isperformed by injecting an electric current into the semiconductor chip.

[0006] As a technique for increasing a transmission capacity by a singleoptical fiber, wavelength division multiplexing (WDM) is known. In asystem adopting WDM, a plurality of optical carriers having differentwavelengths are used. The plural optical carriers are individuallymodulated to thereby obtain a plurality of optical signals, which arewavelength division multiplexed by an optical multiplexer to obtain WDMsignal light, which is output to an optical fiber transmission line. Onthe receiving side, the WDM signal light received is separated intoindividual optical signals by an optical demultiplexer, and transmitteddata is reproduced according to each optical signal. Accordingly, byapplying WDM, the transmission capacity in a single optical fiber can beincreased according to the number of WDM channels.

[0007] In the case of incorporating an optical amplifier into a systemadopting WDM, a transmission distance is limited by a gaincharacteristic (wavelength characteristic of gain) which is often calledas a gain tilt. For example, in an EDFA, a gain deviation is produced atwavelengths in the vicinity of 1.55 μm. When a plurality of EDFAs arecascaded to cause accumulation of gain tilts, an optical SNR(signal-to-noise ratio) in a channel included in a band giving a smallgain is degraded.

[0008] To cope with the gain tilt of an optical amplifier, a gainequalizer may be used. Before a degradation in optical SNR in a certainchannel becomes excessive due to accumulation of gain tilts, gainequalization is performed by the gain equalizer provided at a suitableposition.

[0009] A tunable optical filter is known as an optical device usable asthe gain equalizer. In the tunable optical filter, a wavelengthcharacteristic of transmittance (or loss) (wavelength dependence oftransmittance) is variable. For example, the wavelength characteristicof the tunable optical filter is set or controlled so as to cancel thegain tilt of an optical amplifier, thereby reducing an interchanneldeviation of powers of optical signals at the receiving end.

[0010] Conventionally known is a tunable optical filter having amechanically movable part. In this kind of tunable optical filter, forexample, an angle of incidence of a light beam on an opticalinterference film or a diffraction grating is mechanically changed,thereby changing a center wavelength in a transmission band or a centerwavelength in a rejection band. That is, the shape of a characteristiccurve giving a wavelength characteristic of transmittance changes alonga wavelength axis. Further, a tunable optical filter provided byPhotonics Technologies, Inc. applies a split-beam Fourier filter as thebasic principles to make variable not only the center wavelength, but arejection quantity (transmittance) itself by mechanical means. That is,the shape of a characteristic curve giving a wavelength characteristicof transmittance is variable not only along the wavelength axis, butalong a transmittance axis.

[0011] Further, as a tunable optical filter capable of changing awavelength characteristic of loss by electrical means without using anymechanically movable part, a waveguide type Mach-Zehnder (MZ) opticalfilter and an acousto-optic tunable filter (AOTF) are known, forexample.

[0012] Further, an optical bandpass filter capable of varying a centerwavelength applying a birefringent filter as the basic principles hasbeen proposed (Japanese Patent Laid-open Publication No. 6-130339).

[0013] The tunable optical filter having a mechanically movable part hasdefects such that high-speed operation is difficult and reliability islacking. Further, the MZ optical filter and the AOTF at present havedefects such that (1) a drive voltage is high, (2) a power consumptionis large, (3) a temperature stabilizing device is required to cause anunavoidable enlargement of scale, and (4) reliability cannot beobtained.

[0014] It is therefore desired to design a tunable optical filter thatcan satisfy such conditions that (1) no mechanically movable part isincluded to obtain high reliability, (2) the filter is controllable byelectrical means, and (3) a drive voltage is low and a power consumptionis small.

[0015] As a candidate for the tunable optical filter satisfying theseconditions, a tunable optical filter described in Japanese PatentLaid-open Publication No. 6-130339 is noticeable. This tunable opticalfilter has a variable Faraday rotator for giving a variable Faradayrotation angle, in which the shape of a characteristic curve giving awavelength characteristic of transmittance is changed along thewavelength axis according to a change in the Faraday rotation angle.However, the shape of the characteristic curve cannot be changed alongthe transmittance axis. In the prior applications of the gain equalizer,for example, it is required that a loss depth in a rejection band isvariable, it therefore cannot be said that this tunable optical filteralways have a sufficient performance as a gain equalizer.

SUMMARY OF THE INVENTION

[0016] It is therefore an object of the present invention to provide atunable optical filter in which the shape of a characteristic curvegiving a wavelength characteristic of transmittance changes along thetransmittance axis. The other objects of the present invention willbecome apparent from the following description.

[0017] In accordance with an aspect of the present invention, there isprovided a tunable optical filter comprising first and secondpolarizers, a birefringent element, and a Faraday rotator. Each of thefirst and second polarizers has a transmission axis determining apolarization axis of transmitted polarized light. The birefringentelement is provided between the first and second polarizers to give aphase difference between two orthogonal components of transmittedpolarized light. The phase difference is determined by an optic axis ofthe birefringent element. The Faraday rotator is provided between thefirst and second polarizers to give a variable Faraday rotation angle totransmitted polarized light. The order of arrangement of thebirefringent element and the Faraday rotator and the relative positionalrelation between the optic axis of the birefringent element and thetransmission axis of each of the first and second polarizers are, forexample, set so that the shape of a characteristic curve giving awavelength characteristic of transmittance changes along a transmittanceaxis according to a change in the Faraday rotation angle.

[0018] With this configuration, the order of arrangement and therelative positional relation are set in a specific manner, so that theshape of the characteristic curve is variable along the transmittanceaxis, thus, a loss depth in a rejection band can be changed, therebyachieving one of the objects of the present invention.

[0019] In the present specification, the term of “transmittance” isdefined as a power transmittance.

[0020] The above and other objects, features and advantages of thepresent invention and the manner of realizing them will become moreapparent, and the invention itself will best be understood from a studyof the following description and appended claims with reference to theattached drawings showing some preferred embodiments of the invention.

BRIEF DESCRIPTION OF THE DRAWINGS

[0021]FIG. 1 is a view for illustrating a birefringent filter in theprior art;

[0022]FIGS. 2A and 2B are graphs for illustrating a characteristic of atunable optical filter in the prior art;

[0023]FIGS. 3A and 3B are graphs for illustrating a characteristic of atunable optical filter required;

[0024]FIG. 4 is a view showing a positional relation among members ofthe birefringent filter shown in FIG. 1;

[0025]FIG. 5 is a graph for illustrating (1/λ) approximated by a linearfunction;

[0026]FIG. 6 is a graph showing a change in wavelength characteristic oftransmittance with a change in an angle e defined in FIG. 4;

[0027]FIGS. 7A and 7B are views showing first and second preferredembodiments of the tunable optical filter according to the presentinvention respectively;

[0028]FIG. 8 is a view showing a positional relation among members ofeach preferred embodiment of the tunable optical filter according to thepresent invention;

[0029]FIG. 9 is a graph showing a first example of the wavelengthcharacteristic of transmittance in the present invention;

[0030]FIG. 10 is a graph for illustrating loss tilt;

[0031]FIG. 11 is a graph showing a second example of the wavelengthcharacteristic of transmittance in the present invention;

[0032]FIGS. 12A and 12B are graphs showing a third example of thewavelength characteristic of transmittance in the present invention;

[0033]FIG. 13 is a graph showing a fourth example of the wavelengthcharacteristic of transmittance in the present invention;

[0034]FIGS. 14A and 14B are views showing third and fourth preferredembodiments of the tunable optical filter according to the presentinvention respectively;

[0035]FIG. 15 is a graph showing a fifth example of the wavelengthcharacteristic of transmittance in the present invention;

[0036]FIG. 16 is a graph showing a sixth example of the wavelengthcharacteristic of transmittance in the present invention;

[0037]FIG. 17 is a view showing a fifth preferred embodiment of thetunable optical filter according to the present invention;

[0038]FIG. 18 is a graph showing a seventh example of the wavelengthcharacteristic of transmittance in the present invention;

[0039]FIG. 19 is a view showing a sixth preferred embodiment of thetunable optical filter according to the present invention;

[0040]FIG. 20 is a graph showing an eighth example of the wavelengthcharacteristic of transmittance in the present invention;

[0041]FIG. 21 is a view showing a seventh preferred embodiment of thetunable optical filter according to the present invention;

[0042]FIG. 22 is a view showing an eighth preferred embodiment of thetunable optical filter according to the present invention;

[0043]FIG. 23 is a view showing a ninth preferred embodiment of thetunable optical filter according to the present invention;

[0044]FIGS. 24A and 24B are graphs showing an example of the wavelengthcharacteristic of transmittance obtained by the tunable optical filtershown in FIG. 23;

[0045]FIG. 25 is a view showing a Faraday rotator applicable to thepresent invention;

[0046]FIG. 26 is a view for illustrating magnetic fields andmagnetization in FIG. 25;

[0047]FIG. 27 is a view showing another Faraday rotator applicable tothe present invention;

[0048]FIG. 28 is a view for illustrating magnetic fields andmagnetization in FIG. 27;

[0049]FIG. 29 is a view showing still another Faraday rotator applicableto the present invention;

[0050]FIG. 30 is a view for illustrating magnetic fields andmagnetization in FIG. 29;

[0051]FIG. 31 is a view showing a tenth preferred embodiment of thetunable optical filter according to the present invention;

[0052]FIG. 32 is a view showing an eleventh preferred embodiment of thetunable optical filter according to the present invention;

[0053]FIG. 33 is a view showing a twelfth preferred embodiment of thetunable optical filter according to the present invention;

[0054]FIG. 34A is a view showing a tunable optical filter correspondingto that shown in FIG. 31; and

[0055]FIG. 34B is a view showing a thirteenth preferred embodiment ofthe tunable optical filter according to the present invention.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0056] Some preferred embodiments of the present invention will now bedescribed in detail with reference to the attached drawings.

[0057] A birefringent filter will first be described with reference toFIG. 1 because it is considered useful in understanding theconfiguration and operation of the tunable optical filter according tothe present invention. The birefringent filter shown in FIG. 1 isconfigured by arranging a first polarizer P1, a birefringent plate BP,and a second polarizer P2 in this order on an optical ch OP. Anorthogonal three-dimensional coordinate system (X, Y, Z) having a z axisparallel to the optical path OP is adopted herein. It is assumed thatthe X axis and the Y axis are parallel to the optic axes (C1 axis and C2axis) of the birefringent plate BP respectively, and the angle formedbetween the transmission axis of the first polarizer P1 and the Y axisis 45°. The angle formed between the transmission axis of the secondpolarizer P2 and the Y axis is arbitrary. “The transmission axis of apolarizer” points in a direction of vibration of linearly polarizedlight transmitted through the polarizer, and it is generally defined asan axis determining the polarization axis of polarized light transmittedthrough the polarizer.

[0058] When linearly polarized light transmitted through the firstpolarizer P1 enters the birefringent plate BP, the linearly polarizedlight is separated into a component having a polarization plane parallelto the C1 axis and a component having a polarization plane parallel tothe c2 axis, and these two components propagate in the birefringentplate BP. Upon output from the birefringent plate BP, these twocomponents are combined at a phase difference determined according towavelength. In the case that the thickness of the birefringent plate BPis sufficiently larger than the wavelength of incident light, thepolarization state of the light combined at the output of thebirefringent plate BP differs based on wavelength. That is, the combinedlight can be linearly polarized light, or circularly, or ellipticallypolarized light according to wavelength. The transmittance of the secondpolarizer P2 depends on the polarization state of light incident on thesecond polarizer P2, and therefore differs according to wavelength. Forexample, assuming that the transmission axis of the second polarizer P2is fixed so as to be parallel to linearly polarized light having acertain wavelength, the transmittance of the second polarizer P2 to thelight of this wavelength is 100% in principle. At another wavelength,the transmittance of the second polarizer P2 to linearly polarized lightperpendicular to the transmission axis of the second polarizer P2 is 0%in principle. Further, the transmittance of the second polarizer P2 tocircularly polarized light having another wavelength is 50% inprinciple, and the transmittance of the second polarizer P2 toelliptically polarized light having another wavelength varies accordingto the ellipticity of the elliptically polarized light. Thus, thetransmittance of this birefringent filter varies depending upon thewavelength of incident light.

[0059]FIGS. 2A and 2B are graphs for illustrating a characteristic of aconventional tunable optical filter. In the tunable optical filterdescribed in Japanese Patent Laid-open Publication No. 6-130339, foxexample, a phase shifter including a Faraday rotator and twoquarter-wave plates is provided in place of the birefringent plate BP ofthe birefringent filter shown in FIG. 1, thereby obtaining a wavelengthcharacteristic such that the transmittance periodically changes withwavelength. As shown by solid and broken lines in FIG. 2A, acharacteristic curve giving this wavelength characteristic is variablein shape along the wavelength axis. Accordingly, by using this tunableoptical filter, it is possible to provide an optical bandpass filterwhose characteristic curve is variable in shape along the wavelengthaxis as shown in FIG. 2B.

[0060]FIGS. 3A and 3B are graphs for illustrating a characteristic of atunable optical filter required by the present invention. In FIG. 2A,the shape of the characteristic curve is variable along the wavelengthaxis. In contrast therewith, the tunable optical filter required by thepresent invention has a characteristic curve whose shape is variablealong the transmittance axis as shown in FIG. 3A. More specifically, inconsideration of use as a gain equalizer, it is required to realize anotch filter in which a loss depth in a rejection band is variable asshown as an example in FIG. 3B.

[0061] Now, quantitative analysis will be made on the birefringentfilter shown in FIG. 1 and next developed into showing a method forproviding a tunable optical filter having such a characteristic as shownin FIGS. 3A and 3B. It is now assumed that in the birefringent filtershown in FIG. 1 the transmission axis P1A of the first polarizer P1, theoptic axes (C1 axis and C2 axis) of the birefringent plate BP, and thetransmission axis P2A of the second polarizer P2 are in positionalrelation to each other as shown in FIG. 4. That is, let φ denote theangle formed between the transmission axis P1A and the C2 axis and θdenote the angle formed between the transmission axis P2A and the C2axis.

[0062] When linearly polarized light sin(ωt) enters the birefringentfilter in a direction parallel to the transmission axis P1A, a componentE1 of transmitted light through the birefringent plate BP parallel tothe C1 axis and a component E2 of the transmitted light parallel to theC2 axis can be expressed as follows:

E1=sin φ sin(ωt+ε1)

E2=cos φ sin(ωt+ε2)

[0063] where ε1 and ε2 are the phase delays of the components E1 and E2respectively. The amplitude of light emerging from the second polarizerP2 is given as follows:

E1 sin θ+E2 cos θ=sin φ sin θ sin(ωt+ε1)+cos φ cos θ sin(ωt+ε2)=(sin φsin θ cos ε1+cos φ cos θ cos ε2)sin ωt+(sin φ sin θ sin ε1+cos φ cos θsin ε2)cos ωt

[0064] Accordingly, the intensity I of transmitted light is given asfollows:

I=cos²(φ+θ)+sin(2φ)sin(2θ)cos²((ε1−ε2)/2)

[0065] Letting d denote the thickness of the birefringent plate BP, μdenote the refractive index difference between an ordinary ray and anextraordinary ray in the birefringent plate BP, and λ denote thewavelength, the following equation holds.

(ε1−ε2)/2=πμd/λ

[0066] Accordingly, the intensity I of transmitted light can beexpressed as a function I(λ) of wavelength λ to give Eq. (1).

I(λ)=cos²(φ+θ)+sin(2φ)sin(2θ)cos²(πμd/λ)  (1)

[0067] As understood from Eq. (1), the transmitted light intensity haswavelength dependence and periodically changes with wavelength. If thevalue of wavelength λ is higher than an actually operating wavelengthband, 1/λ can be approximated by a linear function as follows:

1/λ=aλ+b

[0068] If the wavelength band is set to a range of 1500 nm to 1600 nm asshown in FIG. 5, for example, a=−4.165×10⁻⁷ (1/nm²) and b=1.291×10⁻³(1/nm).

[0069] Neglecting b and considering only a relative wavelength, Eq. (1)′is given.

I(λ)=cos²(φ+θ)+sin(2φ)sin(2θ)cos²(πλ/FSR)  (1)′

[0070] where FSR (Free Spectral Range) represents a wavelength period ina wavelength characteristic of transmittance, and it is expressed asfollows:

FSR=1/aμd  (2)

[0071] Accordingly, it is understood that a required FSR can be obtainedby adjusting the thickness d of the birefringent plate BP provided thatthe refractive index difference μ determined by the material of thebirefringent plate BP is constant.

[0072] Eq. (1) shows that the transmitted light intensity changes with achange in angle φand/or angle θ. Referring to FIG. 6, there is shown achange in wavelength characteristic of transmittance in the case thatthe angle θ is changed with the angle φfixed to π/4 (45°), for example.In FIG. 6, the vertical axis represents transmittance (true value) andthe horizontal axis represents relative wavelength normalized by FSR.The signs attached to the values of the angle θ having positive andnegative value are intended to show relative rotational directionsbetween the C2 axis and the transmission axis P2A, which will behereinafter described in detail.

[0073] A direct method for changing the angle θ is to rotate thetransmission axis P2A of the second polarizer P2. In present techniques,any polarizer capable of rotating its transmission axis without usingmechanical means is not known. Although a polarizer capable of rotatingits transmission axis can be provided by using mechanical means, atunable optical filter having a mechanically movable part has problemssuch that high-speed operation is difficult and reliability is lacking.In view of this fact, the present invention has proposed a method usinga variable Faraday rotator as will be hereinafter described in detail.

[0074] The angle θ is an angle formed between the transmission axis P2Aof the second polarizer P2 and the C2 axis, and it can be said that theangle θ is an angle formed between the polarization axis of lightincident on the second polarizer P2 and the transmission axis P2A of thesecond polarizer P2. In other words, “rotating the transmission axis P2Aof the second polarizer P2” is substantially the same as “rotating thepolarization axis of light incident on the second polarizer P2”.Accordingly, by locating a Faraday rotator for giving a variable Faradayrotation angle between the birefringent plate BP and the secondpolarizer P2, and by rotating an azimuth of polarized light incident onthe second polarizer P2, the same condition as that obtained by changingthe angle e can be realized, and the transmitted light intensity cantherefore be changed according to the rotation of the azimuth.

[0075] Similarly, by locating a variable Faraday rotator between thefirst polarizer P1 and the birefringent plate BP, and by rotating anazimuth of polarized light incident on the birefringent plate BP, thesame condition as that obtained by changing the angle φ can be realized,and the transmitted light intensity can therefore be changed accordingto the rotation of the azimuth.

[0076] Referring to FIGS. 7A and 7B, there are shown first and secondpreferred embodiments of the tunable optical filter according to thepresent invention respectively. In the first preferred embodiment shownin FIG. 7A, a variable Faraday rotator FR is provided between thebirefringent plate BP and the second polarizer P2. In the secondpreferred embodiment shown in FIG. 7B, a variable Faraday rotator FR isprovided between the first polarizer P1 and the birefringent plate BP.

[0077] The simplest and clearest requirements for carrying out thetunable optical filter according to the present invention in each of thefirst and second preferred embodiments will now be reconfirmed. In eachpreferred embodiment, the birefringent plate BP and the variable Faradayrotator FR are provided between the first polarizer P1 and the secondpolarizer P2. The first polarizer P1 has a transmission axis P1Adetermining the polarization axis of transmitted polarized light, andthe second polarizer P2 has a transmission axis P2A determining thepolarization axis of transmitted polarized light. The birefringent plateBP has optic axes (C1 axis and C2 axis, or any one of them) determininga phase difference given between two orthogonal components oftransmitted polarized light. The variable Faraday rotator FR gives avariable Faraday rotation angle to transmitted polarized light. Theorder of arrangement of the birefringent plate BP and the variableFaraday rotator FR, and the relative positional relation between theoptic axis (e.g., C1 axis) and the transmission axes P1A and P2A are setso that the shape of a characteristic curve giving a wavelengthcharacteristic of transmittance changes along the transmittance axisaccording to a change in the Faraday rotation angle.

[0078] Further, the thickness of the birefringent plate BP is designedso that a required FSR can be obtained. To realize wavelength dependenceof transmittance, a birefringent plate having a thickness larger thanthat of a quarter-wave plate or a half-wave plate, specifically, havinga thickness sufficiently larger than an operating wavelength, is used asthe birefringent plate BP. More specifically, a birefringent platecapable of giving a phase difference corresponding to a length 20 to 100times an operating wavelength is adopted as the birefringent plate BP.

[0079] In the first preferred embodiment shown in FIG. 7A, input lightis transmitted through the first polarizer P1, the birefringent plateBP, the variable Faraday rotator FR, and the second polarizer P2 in thisorder along the optical path OP.

[0080] In the second preferred embodiment shown in FIG. 7B, input lightis transmitted through the first polarizer P1, the variable Faradayrotator FR, the birefringent plate BP, and the second polarizer P2 inthis order along the optical path OP.

[0081]FIG. 8 shows a positional relation among the members in eachpreferred embodiment of the tunable optical filter according to thepresent invention. It is assumed that in the orthogonalthree-dimensional coordinate system (X, Y, Z) the Z axis is parallel tothe optical path OP, and the Y axis is parallel to the transmission axisP1A of the first polarizer P1. Further, φ, θ, and δ will be definednewly or more precisely as follows:

[0082] φ: angle formed between the C1 axis of the birefringent plate BPand the transmission axis P1A (Y axis) of the first polarizer P1. It isassumed that the angle φtakes a positive sign when rotating clockwisefrom the Y axis toward the C1 axis.

[0083] θ: angle formed between the C1 axis of the birefringent plate BPand the transmission axis P2A of the second polarizer P2. It is assumedthat the angle θ takes a positive sign when rotating clockwise from thetransmission axis P2A toward the C1 axis.

[0084] δ: angle formed between the transmission axis P1A (Y axis) of thefirst polarizer P1 and the transmission axis P2A of the second polarizerP2. It is assumed that the angle δ takes a positive sign when rotatingclockwise from the Y axis toward the transmission axis P2A.

[0085] Accordingly, φ=θ+δ. Further, the Faraday rotation angle a givenby the Faraday rotator FR takes a positive sign when rotatingcounterclockwise from the X axis toward the Y axis.

[0086] In FIG. 8, the group of an ellipse (including a circle) andstraight lines represented by reference symbol PS represents wavelengthdependence of a polarization state at the output of the birefringentplate BP in the case of α=0.

[0087] To make the transmitted light intensity of the tunable opticalfilter have wavelength dependence, the condition that “sin(2φ) sin(2θ)is always zero” must be avoided as apparent from Eq. (1). Therefore, inthe case of providing the same condition as that obtained bysubstantially changing the angle θ by using the Faraday rotator FR asdescribed in the first preferred embodiment shown in FIG. 7A, the angleφmust satisfy φ≢nπ/2 (n is an integer). Further, in the case ofproviding the same condition as that obtained by substantially changingthe angle φ by using the Faraday rotator FR as described in the secondpreferred embodiment shown in FIG. 7B, the angle θ must satisfy θ≢nπ/2(n is an integer).

[0088] According to the optical theory, a polarization state of lightand an operation of an optical element acting on its transmitted lightcan be represented by a 1×2 matrix known as the Jones Vector and a 2×2matrix known as the Jones Matrix. Further, optical power at eachtransmission point can be expressed as the sum of the squares of twocomponents of the Jones Vector. By matrix calculation using the JonesVector and the Jones Matrix, the transmittance (power transmittance) ofthe tunable optical filter according to the present invention can becalculated.

[0089]FIG. 9 shows the results of calculation of a wavelengthcharacteristic of transmittance in the first preferred embodiment shownin FIG. 7A under the conditions that the angles φ and δ are set to φ=n/4and δ=0, and the Faraday rotation angle α is changed. In FIG. 9, thevertical axis represents transmittance (dB) and the horizontal axisrepresents relative wavelength normalized by FSR. As apparent from FIG.9, the shape of the characteristic curve giving the wavelengthcharacteristic of transmittance changes along the transmittance axis(the vertical axis) with a change in the Faraday rotation angle α in thecondition that the points corresponding to relative wavelengths of 0.25and −0.25 are fixed points.

[0090] By changing the Faraday rotation angle α in the range of−δ<α<π/2−δ (range of π/2) in the case of φ=π/4, or in the range of−δ>α>−π/2−δ (range of π/2) in the case of φ=−π/4, all obtainableconditions of the wavelength characteristic of transmittance can berealized.

[0091] According to this relation, it is understood that in the case ofδ=0, that is, in the case that the transmission axes P1A and P2A aremade parallel to each other, it is sufficient to select either apositive sign or a negative sign for the Faraday rotation angle α to bechanged. Accordingly, by setting δ=0, 0<α<π/2 or 0>α>−π/2 is given, sothat a Faraday rotator giving a Faraday rotation angle α in only onedirection can be used, thereby simplifying the configuration of theFaraday rotator FR. This effect is similarly exhibited also in thesecond preferred embodiment shown in FIG. 7B.

[0092] Conversely, by using a variable Faraday rotator capable of givinga Faraday rotation angle a in opposite directions and setting δ=φ, thetransmittance becomes constant irrespective of wavelength when α=0. Forexample, in the case that the tunable optical filter according to thepresent invention is incorporated into a system, there is a case that aconstant transmittance is preferable irrespective of wavelength whencontrol becomes off to result in α=0. In this case, −π/4<α<π/4 holds, sothat the absolute value of the Faraday rotation angle π is smaller thanπ/4. Accordingly, in the case that a variable Faraday rotator applying amagneto-optic effect is used, it is possible to reduce the powerconsumption when the Faraday rotation angle α is set to a maximum value.Similar discussions apply also to the second preferred embodiment shownin FIG. 7B, in which it is sufficient to set δ=θ.

[0093] The tunable optical filter having such a characteristic as shownin FIG. 9 is potentially applied to a power equalizer having a variableloss tilt, for example. The term of “loss tilt” indicates a slope of alinear characteristic curve giving a wavelength characteristic oftransmittance represented by logarithm as shown in FIG. 10. Such a powerequalizer having a variable loss tilt is effective in equalizing gaintilt in an optical amplifier or in compensating for loss tilt in anoptical fiber in an optical fiber communication system, for example.

[0094] In the case of using the tunable optical filter having such acharacteristic as shown in FIG. 9 as an equalizer having a variable losstilt, an average of losses in an operating wavelength band (which willbe hereinafter referred to as “average loss”) can be maintained constantby selecting the operating wavelength band in the following manner, forexample. That is, a center value between adjacent two wavelengths ofsome wavelengths providing a maximum loss or a minimum loss is selectedas a center wavelength in the operating wavelength band, and thebandwidth of the operating wavelength band is set smaller than ½ of FSR.

[0095]FIG. 11 shows an example obtained by selecting a point C whichgives a center value between a point A and a point B each providing amaximum loss or a minimum loss in the graph shown in FIG. 9 as a centerwavelength in the operating wavelength band, and by setting thebandwidth of the operating wavelength band to ⅕ of FSR. As apparent fromFIG. 11, a characteristic with a variable loss tilt is obtained.Further, as also apparent from FIG. 11, the average loss does not changeirrespective of a change in the Faraday rotation angle α. In the graphshown in FIG. 11, a perfect straight line shown by a broken line clearlyindicates that each characteristic curve is substantially linear (asalso in the cases of FIGS. 13 and 16).

[0096] However, the tunable optical filter having the characteristic ofFIG. 11 has a problem that the average loss is as large as 3 dB. Tosolve this problem, the following two methods are considered.

[0097] The first method is a method of making the angle (φ or θ) betweenone of the transmission axes P1A and P2A and the C1 axis of thebirefringent plate BP different from ±π/4.

[0098] For example, in the first preferred embodiment shown in FIG. 7A,the angle φ is set so as to satisfy 0<φ<π/4 and the Faraday rotationangle α is changed in the range of −δ<α<2φ−δ. Alternatively, the angle+is set so as to satisfy −π/4<φ<0 and the Faraday rotation angle α ischanged in the range of −δ>α>2φ−δ.

[0099]FIGS. 12A and 12B show the results of calculation of a wavelengthcharacteristic of transmittance under the conditions that the angles φand δ are set to φ=π/6 and δ=0 and the Faraday rotation angle α ischanged. FIG. 13 shows a wavelength characteristic obtained by enlarginga part of the wavelength characteristic shown in FIGS. 12A and 12B inaccordance with the relative wavelength range shown in FIG. 11. Asapparent from FIG. 13, the average loss is smaller than that of thewavelength characteristic shown in FIG. 11. However, the average losschanges with a change in the Faraday rotation angle a in the example ofFIG. 13.

[0100] In the second preferred embodiment shown in FIG. 7B, the angle θis set so as to satisfy 0<θ<π/4 and the Faraday rotation angle α ischanged in the range of −δ>α>−2θ−δ. Alternatively, the angle θ is set soas to satisfy −π/4<θ<0 and the Faraday rotation angle α is changed inthe range of −δ<α<−2θ−δ. Also in this case, an effect similar to that inthe first preferred embodiment shown in FIG. 7A can be obtained.

[0101] Also in the above case of making the angle φ or θ different from±π/4 according to the first method, a variable Faraday rotator capableof giving a Faraday rotation angle α in only one direction can be usedby setting δ=0. Further, by setting δ=φ in the first preferredembodiment shown in FIG. 7A, or by setting δ=θ in the second preferredembodiment shown in FIG. 7B, the transmittance can be maintainedconstant irrespective of wavelength when control becomes off to resultin α=0.

[0102] The effect obtained by making the angle φ or θ different from±π/4 can be realized also by inserting a quarter-wave plate at a properposition with a proper angle to change a polarization orientation asshown in each of FIGS. 14A and 14B.

[0103]FIG. 14A shows a third preferred embodiment of the tunable opticalfilter according to the present invention. In contrast with the firstpreferred embodiment shown in FIG. 7A, the third preferred embodiment ischaracterized in that a quarter-wave plate 2 is additionally providedbetween the first polarizer P1 and the birefringent plate BP.

[0104]FIG. 14B shows a fourth preferred embodiment of the tunableoptical filter according to the present invention. In contrast with thesecond preferred embodiment shown in FIG. 7B, the fourth preferredembodiment is characterized in that a quarter-wave plate 2 isadditionally provided between the birefringent plate BP and the secondpolarizer P2.

[0105] The second method is a method of using a partial polarizer as thesecond polarizer P2. The term of “partial polarizer” refers to apolarizer indicating a transmittance value not equal to 0(antilogarithm) upon incidence of linearly polarized light having apolarization plane orthogonal to the transmission axis. In the partialpolarizer, the transmittance of linearly polarized light having apolarization plane orthogonal to the transmission axis is defined as t.

[0106]FIG. 15 shows the results of calculation of a wavelengthcharacteristic of transmittance by using a partial polarizer having atransmittance t=0.25 (−6 dB) as the second polarizer P2 under theconditions that the angles φ and δ are set to φ=π/4 and δ=0 and theFaraday rotation angle α is changed.

[0107]FIG. 16 shows a wavelength characteristic obtained by enlarging apart of the wavelength characteristic shown in FIG. 15. As compared withthe characteristic shown in FIG. 11, the average loss is smaller in thecharacteristic shown in FIG. 16. Furthermore, the average loss does notchange with a change in the Faraday rotation angle a.

[0108] In the case of carrying out the second method in the firstpreferred embodiment shown in FIG. 7A, a variable amount (a variablerange of transmittance at a certain wavelength) can be maximized bysetting φ=±π/4, because all obtaintable conditions of the wavelengthcharacteristic of transmittance can be realized as previously mentioned.In the case of carrying out the second method in the second preferredembodiment shown in FIG. 7B, a variable amount can similarly bemaximized by setting θ=±π/4.

[0109] Also in the case of carrying out the second method, a variableFaraday rotator capable of giving a Faraday rotation angle in only onedirection can be used by setting δ=0. Further, by setting δ=φ in thefirst preferred embodiment shown in FIG. 7A, or by setting δ=θ in thesecond preferred embodiment shown in FIG. 7B, the transmittance can bemaintained constant irrespective of wavelength when control becomes offto result in α=0.

[0110] The first and second methods are effective also in giving afinite value to the maximum loss. For example, in the case of settingφ=π/4 in the first preferred embodiment shown in FIG. 7A, the powertransmittance takes 0 (antilogarithm) in principle, so that the maximumloss (dB) becomes infinite as apparent from FIG. 9. In some case, such acharacteristic is undesirable in operating a system. By using the firstor second method, the maximum loss (dB) can be suppressed to a finitevalue. This will become apparent from FIGS. 12A and 12B and FIG. 15.

[0111]FIG. 17 shows a fifth preferred embodiment of the tunable opticalfilter according to the present invention. In each of the previouspreferred embodiments, a single variable Faraday rotator FR is used. Incontrast therewith, the fifth preferred embodiment is characterized inthat two variable Faraday rotators FR1 and FR2 are provided between thefirst polarizer P1 and the second polarizer P2. The birefringent plateBP is provided between the Faraday rotators FR1 and FR2. Thisconfiguration can provide a wavelength characteristic different fromeach wavelength characteristic mentioned above.

[0112] For example, consider the case of rotating a Faraday rotationangle α1 given by the Faraday rotator FR1 and a Faraday rotation angleα2 given by the Faraday rotator FR2 with the relation of α1=α2maintained under the conditions that the angles φ and δ are set toφ=±π/4 and δ=nπ/2 (n is an integer). Input light is transmitted throughthe first polarizer P1, the Faraday rotator FR1, the birefringent plateBP, the Faraday rotator FR2, and the second polarizer P2 in this orderalong the optical path OP.

[0113]FIG. 18 shows a wavelength characteristic of transmittance in thecase of rotating the Faraday rotation angle α (α1 and α2) in the rangeof 0<α<π/4 under the conditions that the angle φ and δ are set to φ=π/4and δ=0. In this case, a partial polarizer is used as the secondpolarizer P2. As apparent from FIG. 18, the minimum loss in thewavelength characteristic of transmittance is always zero irrespectiveof the Faraday rotation angle α.

[0114] To change each Faraday rotation angle with the relation of α1=α2maintained, the fifth preferred embodiment shown in FIG. 17 employs acontrol unit 4 connected to the Faraday rotators FR1 and FR2. Thecontrol unit 4 controls the Faraday rotators FR1 and FR2 so that theFaraday rotation angle α1 given by the Faraday rotator FR1 and theFaraday rotation angle α2 given by the Faraday rotator FR2 becomesubstantially equal to each other.

[0115]FIG. 19 shows a sixth preferred embodiment of the tunable opticalfilter according to the present invention. In each of the previouspreferred embodiments, a single birefringent plate BP is used. Incontrast therewith, the sixth preferred embodiment is characterized inthat two birefringent plates BP1 and BP2 are provided between the firstpolarizer P1 and the second polarizer P2. The variable Faraday rotatorFR is provided between the birefringent plates BP1 and BP2. Input lightis transmitted through the first polarizer p1, the birefringent plateBP1, the Faraday rotator FR, the birefringent plate BP2, and the secondpolarizer P2 in this order along the optical path OP.

[0116] By using the two birefringent plates BP1 and BP2, a wavelengthcharacteristic like the wavelength characteristic shown in FIG. 18 canbe obtained. For example, angles φ1 and φ2 are defined with respect tothe optic axes of the birefringent plates BP1 and BP2 respectively, assimilarly to the angle φ mentioned above, and the angles φ1 and φ2 areset equal to each other (φ1=φ2). Further, the angles φ1, φ2, and δ areset to φ1=±π/4, φ2=±π/4, and δ=nπ/2 (n is an integer).

[0117]FIG. 20 shows a wavelength characteristic of transmittance in thecase of rotating the Faraday rotation angle a given by the Faradayrotator FR in the range of 0<α<π/2 under the conditions that the anglesφ1, φ2, and δ are set to φ1=φ2=π/4 and δ=0. In this case, a partialpolarizer is used as the second polarizer P2. As apparent from FIG. 20,the minimum loss in the wavelength characteristic of transmittance isalways zero irrespective of the Faraday rotation angle α.

[0118] Also in the sixth preferred embodiment shown in FIG. 19, aFaraday rotator capable of giving a variable Faraday rotation angle inonly one direction can be used by setting δ=0.

[0119]FIG. 21 shows a seventh preferred embodiment of the tunableoptical filter according to the present invention. This preferredembodiment is characterized in that a variable phase shifter 6 isadditionally provided between the first polarizer P1 and the secondpolarizer P2. The variable phase shifter 6 gives a phase difference(retardation) between a polarization component parallel to its opticaxis and a polarization component orthogonal to its optic axis. Thephase difference is made variable by a control signal supplied to thevariable phase shifter 6. The first polarizer P1, the birefringent plateBP, the variable Faraday rotator FR, and the second polarizer P2 arearranged in accordance with the first preferred embodiment shown in FIG.7A. Further, the variable phase shifter 6 is provided between the firstpolarizer P1 and the birefringent plate BP.

[0120] According to the preferred embodiment shown in FIG. 21, the shapeof a characteristic curve giving a wavelength characteristic oftransmittance changes not only with a change in the Faraday rotationangle given by the variable Faraday rotator FR along the transmittanceaxis, but also with a change in the phase difference given by thevariable phase shifter 6 along the wavelength axis. consequently, notonly the characteristic of the tunable optical filter described withreference to FIGS. 3A and 3B, but also the characteristic of the tunableoptical filter described with reference to FIGS. 2A and 2B can beobtained.

[0121] To most effectively change the shape of the characteristic curvealong the wavelength axis, it is preferable to set the angle between theoptic axis of the variable phase shifter 6 and the optic axis of thebirefringent plate BP to nπ/2 (n is an integer).

[0122] As the variable phase shifter 6, an optical element applying anelectro-optic effect such as LiNbO₃ may be adopted. However, such avariable phase shifter applying an electro-optic effect requires a highdrive voltage in general.

[0123]FIG. 22 shows an eighth preferred embodiment of the tunableoptical filter according to the present invention. This preferredembodiment employs a variable phase shifter 6 having a specificconfiguration to aim at decreasing the drive voltage for the variablephase shifter 6. The variable phase shifter 6 shown in FIG. 22 includestwo quarter-wave plates 10 and 12 and another variable Faraday rotator 8provided between the quarter-wave plates 10 and 12. The angle formedbetween the optic axis of the quarter-wave plate 10 and the optic axisof the quarter-wave plate 12 is set to π/2. By setting the angle betweenthe optic axis of each of the quarter-wave plates 10 and 12 and theoptic axis of the birefringent plate BP to nπ/2 (n is an integer), theshape of a characteristic curve giving a wavelength characteristic oftransmittance of this tunable optical filter can be changed with achange in the Faraday rotation angle given by the variable Faradayrotator 8 along the wavelength axis.

[0124] In the case that the Faraday rotation angle given by the Faradayrotator 8 is β, the phase difference between two orthogonal componentsof polarized light given by the variable phase shifter 6 becomes 2β. Theprinciple of this is apparent from the contents disclosed in JapanesePatent Laid-open Publication No. 6-130339 and from the known art, so thedescription thereof will be omitted herein.

[0125]FIG. 23 shows a ninth preferred embodiment of the tunable opticalfilter according to the present invention. In contrast with the eighthpreferred embodiment shown in FIG. 22, the ninth preferred embodiment ischaracterized in that at least one filter unit is additionally providedbetween the first polarizer P1 and the second polarizer P2. Morespecifically, N set (N is an integer greater than 1) of filter units 14(#1 to #N) are provided. Of these filter units 14 (#1 to #N), the i-th(i is an integer satisfying 1≦i≦N) filter unit 14 (#i) includes apolarizer P1 (#i), a variable phase shifter 6 (#i), a birefringent plateBP (#i), and a Faraday rotator FR (#i) corresponding to the firstpolarizer P1, the variable phase shifter 6, the birefringent plate BP,and the variable Faraday rotator FR, respectively.

[0126] The wavelength characteristic of transmittance of this tunableoptical filter as a whole is given as the sum of the wavelengthcharacteristic of transmittance of the tunable optical filter shown inFIG. 22 and the wavelength characteristic of transmittance of eachfilter unit 14 (#1 to #N). Accordingly, the wavelength characteristic oftransmittance can be easily arbitrarily set.

[0127] For example, in the case that three characteristic curves eachgiving a wavelength characteristic of transmittance are obtained in thetunable optical filter of FIG. 23 as shown in FIG. 24A, the totalwavelength characteristic of transmittance is given as the sum of thethree characteristic curves, so that a desired wavelength characteristicof transmittance can be obtained as shown in FIG. 24B.

[0128] While each filter unit 14 (#i) having the variable phase shifter6 (#i) for changing a characteristic curve along the wavelength axis andthe birefringent plate BP (#i) and the Faraday rotator FR (#i) forchanging a characteristic curve along the transmittance axis areutilized in this preferred embodiment, either the variable phase shifter6 (#i) or the birefringent plate BP (#i) and the Faraday rotator FR (#i)may be omitted as required.

[0129] Some specific embodiments of the Faraday rotator for giving avariable Faraday rotation angle will now be described.

[0130] In general, when linearly polarized light, for example, passesthrough a magneto-optic crystal in the condition where a certainmagnetic field is applied to the magneto-optic crystal, i.e., in thecondition where the magneto-optic crystal is placed in a certainmagnetic field, a polarization direction of the linearly polarized light(defined as a projection of a plane containing an electric field vectorof the linearly polarized light onto a plane perpendicular to apropagation direction of the linearly polarized light) is rotated alwaysin a fixed direction irrespective of the propagation direction. Thisphenomenon is called Faraday rotation, and the magnitude of an angle ofrotation of the polarization direction (Faraday rotation angle) dependson a direction and strength of magnetization of the magneto-opticcrystal generated by the applied magnetic field. More specifically, theFaraday rotation angle is determined by a size of a component of thestrength of magnetization of the magneto-optic crystal in the lightpropagation direction. Accordingly, by configuring a Faraday rotatorwith a magneto-optic crystal and means for applying a magnetic field tothe magneto-optic crystal in the same direction as the light propagationdirection, it appears that the Faraday rotation angle can be effectivelyadjusted by adjusting the applied magnetic field.

[0131] However, it should be considered herein that when the magnitudeof the applied magnetic field is relatively small, the strength ofmagnetization of the magneto-optic crystal by the applied magnetic fielddoes not reach a saturated condition, but many magnetic domains arepresent in the magneto-optic crystal. The presence of such many magneticdomains deteriorate reproducibility of the Faraday rotation angle, ormakes it difficult to continuously vary the Faraday rotation angle eventhough good reproducibility is ensured. Furthermore, when many magneticdomains are present in the magneto-optic crystal, there occursattenuation due to light scattering at an interface between any adjacentmagnetic domains, causing a disadvantage in practical use.

[0132] In a preferred embodiment of the present invention intended tosolve this problem, the variable Faraday rotator includes amagneto-optic crystal located on an optical path, magnetic fieldapplying means for applying first and second magnetic fields havingdifferent directions to the magneto-optic crystal so that the strengthof a synthetic magnetic field of the first and second magnetic fieldsbecomes larger than a predetermined value (e.g., a value correspondingto the strength of a magnetic field required to saturate the strength ofmagnetization of the magneto-optic crystal), and magnetic fieldadjusting means for changing at least one of the first and secondmagnetic fields.

[0133] The condition where the strength of magnetization of themagneto-optic crystal has been saturated can be understood as acondition where the magnetic domains in the magneto-optic crystal hasbecome a single magnetic domain.

[0134] Preferably, the first and second magnetic fields are applied inorthogonal directions in a plane containing a propagation direction oflight passing through the magneto-optic crystal.

[0135]FIG. 25 shows a variable Faraday rotator 32 applicable to thepresent invention. The variable Faraday rotator 32 is usable as thevariable Faraday rotator FR or the variable Faraday rotator 8. TheFaraday rotator 32 includes a magneto-optic crystal 41, a permanentmagnet 42 and an electromagnet 43 for applying magnetic fields inorthogonal directions to the magneto-optic crystal 41, and a variablecurrent source 44 for giving a drive current to the electromagnet 43.

[0136] By using a thin slice of YIG (Yttrium-Iron-Garnet) or anepitaxially grown crystal of (GdBi)₃(FeAlGa)₅O₁₂, as the magneto-opticcrystal 41, for example, the drive current can be reduced.

[0137] The thickness direction of the magneto-optic crystal 41 isparallel to the Y axis, for example. In this case, the directions of themagnetic fields applied to the magneto-optic crystal 41 by the permanentmagnet 42 and the electromagnet 43 are parallel to the Z axis and the Xaxis respectively. Reference numeral 45 denotes a light beam passingthrough the magneto-optic crystal 41.

[0138]FIG. 26 is a view for illustrating the direction and strength(magnitude) of the magnetic field applied to the magneto-optic crystal41, and of the magnetization of the magneto-optic crystal 41 in theFaraday rotator 32 shown in FIG. 25.

[0139] In the case that a magnetic field vector 51 is applied to themagneto-optic crystal 41 by the permanent magnet 42 only, amagnetization vector in the magneto-optic crystal 41 is parallel to theZ axis as shown by reference numeral 52. In this case, the strength ofthe applied magnetic field (the length of the magnetic field vector 51)is set so that the strength of the magnetization of the magneto-opticcrystal 41 (the length of the magnetization vector 52) is saturated. Itis assumed that a required maximum Faraday rotation angle is obtained inthis condition.

[0140] When a magnetic field vector 53 is applied parallel to the X axisby the electromagnet 43, the synthetic magnetic field is given as asynthetic vector of the magnetic field vectors 51 and 53 as shown byreference numeral 54. This synthetic magnetic field 54 generates amagnetization vector 55 in the magneto-optic crystal 41. Themagnetization vector 55 and the magnetic field vector 54 are parallel toeach other, and the length of the magnetization vector 55 is equal tothe length of the magnetization vector 52.

[0141] Although the strength of the magnetization of the magneto-opticcrystal 41 is fixed, a degree of contribution of the magnetization ofthe magneto-optic crystal 41 to the Faraday rotation angle is not alwaysthe same, because the Faraday rotation angle depends also upon therelation between the direction of the magnetization and the lightpropagation direction. That is, in comparing to the condition of themagnetization vector 52 with the condition of the magnetization vector55, a z component 56 of the magnetization vector 55 is smaller than a Zcomponent (the magnetization vector 52 itself) of the magnetizationvector 52. Incidentally, the Faraday rotation angle corresponding to themagnetization vector 55 is smaller than that corresponding to themagnetization vector 52.

[0142] According to this preferred embodiment, the strength of themagnetization of the magneto-optic crystal 41 is always saturated overthe whole variable range of the Faraday rotation angle, therebyeliminating the disadvantage caused by formation of many magneticdomains in the magneto-optic crystal 41. That is, reproducibility of theFaraday rotation angle can be improved, and the Faraday rotation anglecan be continuously changed. Further, by adjusting the drive currentsupplied from the variable current source 44, the Faraday rotation anglecan be changed continuously with good reproducibility. Accordingly, byapplying the Faraday rotator 32 to the present invention, it is possibleto provide a tunable optical filter which can be operated at high speedsand has high reliability.

[0143] Accordingly, by applying such a variable Faraday rotator to thepresent invention, it is possible to provide a tunable optical filterwhose wavelength characteristic of transmittance is well reproducibleand continuously variable.

[0144]FIG. 27 shows another Faraday rotator 32′ applicable to thepresent invention. The Faraday rotator 32′ is different from the Faradayrotator 32 shown in FIG. 25 in the point that parallel plane surfaces 61and 62 are formed at opposite edges of a rectangular magneto-opticcrystal 41 and that a light beam 63 is passed through the plane surfaces61 and 62. Accordingly, both the direction of a magnetic field by thepermanent magnet 42 and the direction of a magnetic field by theelectromagnet 43 are inclined about 450 to a light propagation direction(parallel to the Z axis).

[0145]FIG. 28 is a view for illustrating the direction and strength ofthe magnetic field applied to the magneto-optic crystal 41 and of themagnetization of the magneto-optic crystal 41 in the Faraday rotator 32′shown in FIG. 27. The magnetic field applied by the electromagnet 43 isadjustable in strength and direction in the range between a conditionshown by reference numeral 71 and a condition shown by reference numeral72. Reference numeral 73 denotes a magnetic field applied by thepermanent magnet 42. In this case, the synthetic magnetic field changesin strength and direction in the range between a condition shown byreference numeral 74 and a condition shown by reference numeral 75. Inassociation therewith, the magnetization of the magneto-optic crystal 41changes in strength and direction in the range between a condition shownby reference numeral 76 and a condition shown by reference numeral 77.By using the Faraday rotator 32′, the variable range of the Faradayrotation angle can be increased without much increasing the variablerange for the drive current of the electromagnet 43.

[0146] The applied magnetic field by the permanent magnet 42 is set sothat the strength of the magnetization of the magneto-optic crystal 41is sufficiently saturated in a condition shown by reference numeral 78where the strength of the magnetization is minimized (the appliedmagnetic field by the electromagnet 43 is zero).

[0147]FIG. 29 shows still another variable Faraday rotator 32″applicable to the present invention. The Faraday rotator 32″ isdifferent from the Faraday rotator 32 shown in FIG. 25 in the point thatan electromagnet 81 is provided in place of the permanent magnet 42shown in FIG. 25 and that a variable current source 82 is additionallyprovided to apply a drive current to the electromagnet 81.

[0148]FIG. 30 is a view for illustrating the direction and strength ofthe magnetic field applied to the magneto-optic crystal 41 and of themagnetization of the magneto-optic crystal 41 in the Faraday rotator 32″shown in FIG. 29. According to the preferred embodiment shown in FIG.29, the synthetic magnetic field can be changed continuously asmaintaining saturation magnetization as shown by reference numerals 91to 94 by adjusting the applied magnetic fields by the electromagnets 43and 81. In association therewith, the magnetization of the magneto-opticcrystal 41 changes continuously as shown by reference numerals 95 to 98.According to the preferred embodiment shown in FIG. 30, the variablerange of the Faraday rotation angle can be easily increased withoutusing a complex-shaped magneto-optic crystal as shown in FIG. 27.

[0149] In the case of using the Faraday rotator 32″, the sense of a Zcomponent of the magnetization of the magneto-optic crystal 41 can bechanged by changing the polarity of the variable current source 44 or82. Accordingly, the direction of Faraday rotation can be changed asrequired. For example, the Faraday rotation angle can be changed in therange of ±45n° (n is a positive integer) with respect to 0°.Accordingly, by applying the Faraday rotator 32″ to the presentinvention and setting the angle δ to δ=φ or δ=θ as mentioned previously,for example, the transmittance can be maintained constant irrespectiveof wavelength when the Faraday rotation angle is 0°. For example, whenthe Faraday rotator 32″ is incorporated into a system and controlbecomes off to shut off the variable current sources 44 and 82, theFaraday rotation angle becomes 0°. Accordingly, the transmittancebecomes constant irrespective of wavelength, thereby facilitatingrestart of the system.

[0150]FIG. 31 shows a tenth preferred embodiment of the tunable opticalfilter according to the present invention. In this preferred embodiment,wedge plates 121 and 122 each formed of a birefringent material are usedas the first polarizer P1 and the second polarizer P2 respectively. Inassociation therewith, this preferred embodiment further includes anoptical fiber 123, a lens 124 for changing a beam parameter of lightemerging from the optical fiber 123 (e.g., collimating the emerginglight) to supply the light beam to the wedge plate 121, a lens 125 forconverging a light beam from the wedge plate 122, and an optical fiber126 to which the light beam converged by the lens 125 is coupled undergiven conditions.

[0151] The wedge plates 121 and 122 are arranged so that a top portionand a bottom portion of the wedge plate 121 are opposed to a bottomportion and a top portion of the wedge plate 122 respectively, andcorresponding surfaces of the wedge plates 121 and 122 are parallel toeach other. That is, the wedge plates 121 and 122 have the same shape.

[0152] For example, the optic axis of the wedge plate 121 is parallel tothe Y axis, and the optic axis of the wedge plate 122 is parallel to theY axis.

[0153] The transmittance axis of each of the wedge plates 121 and 122 aspolarizers is defined as a polarization direction of an extraordinaryray whose polarization plane is parallel to the optic axis, or apolarization direction of an ordinary ray whose polarization plane isperpendicular to the optic axis.

[0154] Light emerging from an excitation end of the optical fiber 123 iscollimated by the lens 124 to become a parallel light beam. This beam isdenoted by reference numeral 130 with its beam thickness neglected. Thebeam 130 is separated into a beam 131 corresponding to the ordinary rayand a beam 132 corresponding to the extraordinary ray in the wedge plate121.

[0155] The beams 131 and 132 are transmitted through the birefringentplate BP and the variable Faraday rotator FR in this order to becomebeams 133 and 134 respectively. The polarization states of the beams 133and 134 are determined by the Faraday rotation angle given by theFaraday rotator FR.

[0156] The beam 133 is separated into beams 135 and 136 respectively,corresponding to the ordinary ray and the extraordinary ray in the wedgeplate 122. The beam 134 is separated into beams 137 and 138respectively, corresponding to the extraordinary ray and the ordinaryray in the wedge plate 122.

[0157] In considering the history of refractions in the past of thebeams 135 to 138 and the shape and arrangement of the wedge plates 121and 122, the beams 135 and 137 are parallel to each other and the beams136 and 138 are not parallel to each other. Accordingly, only the beams135 and 137 can be focused through the lens 125 to be coupled to anexcitation end of the optical fiber 126.

[0158] The ratio of the total power of the beams 135 and 137 and thetotal power of the beams 136 and 138 depends on the Faraday rotationangle given by the Faraday rotator FR. For example, in the case that thebeams 133 and 134 are linearly polarized light having the samepolarization planes as those of the beams 131 and 132 respectively, thebeams 133 and 134 are entirely converted into the beams 135 and 137respectively. In the case that the beams 133 and 134 are linearlypolarized light having polarization planes orthogonal to thepolarization planes of the beams 131 and 132 respectively, the beams 133and 134 are entirely converted into the beams 136 and 138 respectively.

[0159] When the Faraday rotation angle given by the Faraday rotator FRis constant, the total power of the beams 135 and 137 is not dependentupon the polarization state of the beam 130. As apparent from theprevious description, the total power of the beams 135 and 137 dependson their wavelengths.

[0160] According to this preferred embodiment, the transmittance of thetunable optical filter can therefore be made independent of thepolarization state of input light. That is, it is possible to provide apolarization-independent tunable optical filter.

[0161]FIG. 32 shows an eleventh preferred embodiment of the tunableoptical filter according to the present invention. In this preferredembodiment, a wedge plate 141 formed of a birefringent material is usedas the first polarizer P1, and two wedge plates 142 and 143 each formedof a birefringent material are used as the second polarizer P2. A topportion and a bottom portion of the wedge plate 141 are opposed to abottom portion and a top portion of the wedge plate 142 respectively. Atop portion and a bottom portion of the wedge plate 143 are opposed tothe bottom portion and the top portion of the wedge plate 142respectively.

[0162] By letting θ1, θ2, and θ3 denote the wedge angles of the wedgeplates 141, 142, and 143; d1 denote the distance between the wedgeplates 141 and 142, and d2 denote the distance between the wedge plates142 and 143, each wedge plate is formed and arranged in order to satisfythe following two equation.

θ2=θ1+θ3, d1 sin θ1=d2 sin θ3

[0163] The optic axis of the wedge plate 141 is parallel to the Y axis,and the optic axes of the wedge plates 142 and 143 are parallel to eachother. The optic axes of the wedge plates 142 and 143 are parallel tothe Y axis, for example.

[0164] In the preferred embodiment shown in FIG. 31, the distancebetween the wedge plates 121 and 122 is necessarily relatively large,because the birefringent plate BP and the Faraday rotator FR areprovided between the wedge plates 121 and 122. Accordingly, the distancebetween the beams 135 and 137 becomes relatively large, so that thebeams 135 and 137 are readily affected by the aberration of the lens 125such as spherical aberration.

[0165] According to the preferred embodiment shown in FIG. 32, a beamfrom the lens 124 is separated by the wedge plate 141 and next beingcombined by the wedge plates 142 and 143. At this time, the opticalpaths of an ordinary ray component and an extraordinary ray componentoutput from the wedge plate 143 are made substantially coincident witheach other. Consequently, these components can be efficiently input intothe optical fiber 126 by the lens 125 with almost no influence of itsaberration.

[0166]FIG. 33 shows a twelfth preferred embodiment of the tunableoptical filter according to the present invention. In this preferredembodiment, two parallel-plane plates 151 and 152 each formed of abirefringent material are used as the first polarizer P1 and the secondpolarizer P2 respectively. The parallel-plane plates 151 and 152 havethe same thickness. The optic axes of the parallel-plane plates 151 and152 are set so that they are orthogonal to each other and each opticaxis is inclined 45° to the Z axis.

[0167] The transmission axis of each of the parallel-plane plates 151and 152 as polarizers is defined as a polarization direction of anextraordinary ray whose polarization plane is parallel to the optic axisor a polarization direction of an ordinary ray whose polarization planeis perpendicular to the optic axis.

[0168] Light emerging from the excitation end of the optical fiber 123is changed in its beam parameter by the lens 124 to become a convergingbeam 160, for example. The beam 160 is separated into beams 161 and 162respectively, corresponding to the ordinary ray and the extraordinaryray in the parallel-plane plate 151. The beams 161 and 162 are parallelto each other. The beams 161 and 162 are transmitted through thebirefringent plate BP and the Faraday rotator FR in this order to becomebeams 163 and 164 respectively. The polarization states of the beams 163and 164 are determined according to the Faraday rotation angle given bythe Faraday rotator FR. The beam 163 is separated into beams 165 and 166respectively, corresponding to the ordinary ray and the extraordinaryray in the parallel-plane plate 152. The beam 164 is separated intobeams 167 and 168 respectively, corresponding to the ordinary ray andthe extraordinary ray in the parallel-plane plate 152.

[0169] The beam 165 comes into coincidence with the beam 168 because theparallel-plane plates 151 and 152 are parallel to each other and havethe same thickness along the Z axis. Accordingly, only the beams 165 and168 can be converged by the lens 125 to enter the optical fiber 126. Theratio between the total power of the beams 165 and 168 and the totalpower of the beams 166 and 167 depends on the Faraday rotation anglegiven by the Faraday rotator FR.

[0170] When the Faraday rotation angle given by the Faraday rotator FRis constant, the total power of the beams 165 and 168 is not dependentupon the polarization state of the beam 160. As apparent from theprevious description, the total power of the beams 165 and 168 dependson their wavelengths.

[0171] Also according to this preferred embodiment, it is possible toprovide a polarization-independent tunable optical filter.

[0172] In the case of using a parallel-plane plate formed of abirefringent material as each polarizer, various arrangements may beadopted by additionally providing a half-wave plate.

[0173]FIGS. 34A and 34B illustrate a thirteenth preferred embodiment ofthe tunable optical filter according to the present invention. FIG. 34Acorresponds to the tenth preferred embodiment shown in FIG. 31, and FIG.34B shows the thirteenth preferred embodiment.

[0174] In the configuration shown in FIG. 34A, each of the wedge plates121 and 122 has a polarization separation angle or wedge angle θ′. Thebeams 135 and 137 are coupled to the optical fiber 126 by the lens 125,but the beams 136 and 138 are not coupled to the optical fiber 126.

[0175] In the thirteenth preferred embodiment shown in FIG. 34B, wedgeplates 121′ and 122′ each having a wedge angle θ″ smaller than the wedgeangle θ′ are used. Beams 135′ to 138′ are output from the wedge plate122′. The beams 135′ and 137′ are entirely coupled to the optical fiber126 by the lens 125 in principle. Because the wedge angle θ″ is smallerthan the wedge angle θ′, the beams 136′ and 138′ originally unexpectedto be coupled to the optical fiber 126 may be partially coupled to theoptical fiber 126. If such partial coupling of the beams 136′ and 138′occurs, it is possible to obtain an effect similar to that obtained byusing a partial polarizer as the second polarizer P2.

[0176] The condition for partially coupling the beams 136′ and 138′ tothe optical fiber 126 is given by a >f sin θ″ where a is the corediameter of the optical fiber 126 and f is the focal length of the lens125. By satisfying this condition, the average loss of the tunableoptical filter can be reduced as in the case of using a partialpolarizer as the second polarizer P2.

[0177] Having thus described various preferred embodiments of thepresent invention, two or more of the above preferred embodiments may becombined to carry out the present invention.

[0178] As described above, according to the present invention, it ispossible to provide a tunable optical filter in which the shape of acharacteristic curve giving a wavelength characteristic of transmittancechanges along the transmittance axis. The other effects by the presentinvention become apparent from the above description.

[0179] The present invention is not limited to the details of the abovedescribed preferred embodiments. The scope of the invention is definedby the appended claims and all changes and modifications as fall withinthe equivalence of the scope of the claims are therefore to be embracedby the invention.

What is claimed is:
 1. An optical filter comprising: a filter filteringa light and having a controllable optical transmittance; and acontroller controlling the optical transmittance of the filter to have afixed amount of transmittance at a specific wavelength.
 2. An opticalfilter comprising: a filter filtering a light and having a controllableoptical transmittance; and a controller controlling the opticaltransmittance of the filter to have a minimum optical transmittance anda maximum optical transmittance at the same specific wavelength.
 3. Anoptical filter comprising: a filter filtering a light and having acontrolling optical transmittance; a controller controlling the opticaltransmittance of the filter to have a constant center of gravitywavelength.
 4. A method comprising: controlling an amount of opticaltransmittance in accordance with a cyclical optical transmittance curve;and controlling a fixed amount of optical transmittance at a specificwavelength in accordance with the curve.
 5. A method of controlling acyclical optical transmittance curve comprising: controlling an amountof optical transmittance in accordance with the curve; and controlling aminimum optical transmittance and a maximum optical transmittance to beat the same specific wavelength in accordance with the curve.
 6. Amethod of controlling a cyclical optical transmittance curve comprising:controlling an amount of optical transmittance in accordance with thecurve; and controlling a center of gravity wavelength to be constant inaccordance with the curve.